**4. X-ray Diffraction characterization of Films**

172 Recent Advances in Crystallography

**Ortho-**

**25-46** 

**System Space**

**System Space** 

**System Space** 

**Cubic** 

**Group** 

**(hexagonal** 

**Group** 

**149-155**

**Point** 

**Table 1.** Symmetry of the planes of a point group. Orientations that lack mirror symmetry (i.e. having

**System Space Group Point Group {100} {010} {001} {0kl} {h0l} {hk0} {hkl} Triclinic 1 1** 1 1 1 1 1 1 1  **2 1** 2 2 2 2 2 2 2 **Monoclinic 3-5 2** m 2 m 1 m 1 1 **(2nd setting) 6-9 m** m 1 m 1 m 1 1  **10-15 2/m** 2mm 2 2mm 2 2mm 2 2

**rhombic 16-24 222** 2mm 2mm 2mm m m m 1

**Tetragonal 75-80 4** 4 m m m 1 1 1  **81-82 4** 4 m m m 1 1 1  **83-88 4/m** 4 2mm 2mm 2mm 2 2 2  **89-98 422** 4mm 2mm 2mm m m m 1  **99-110 4mm** 4mm m m m m m 1  **111-122 42m** 4mm m 2mm m m m 1  **123-142 4m2** 4mm 2mm 2mm 2mm 2mm 2mm 2

**Trigonal 143-146 3** 3 1 1 1 1 1 1

**axes) 147-148 3** 6 2 2 2 2 2 2

 **312** 3m1 2 m 1 1 m 1  **156-161 3m1** 3m1 m 1 1 m 1 1

**Hexagonal 168-173 6** 6 m m m 1 1 1  **174 6** 3 m m m 1 1 1  **175-176 6/m** 6 2mm 2mm 2mm 2 2 2  **177-182 622** 6mm 2mm 2mm m m m 1  **183-186 6mm** 6mm m m m m m 1 **187-190 6m2** 3m1 2mm m m m m 1 **62m** 31m m 2mm m m m 1

 **191-194 6/mmm** 6mm 2mm 2mm 2mm 2mm 2mm 2

**195-199 23** 2mm 3 m m 1 1 1 **200-206 m3** 2mm 6 2mm 2mm 2 2 2  **207-214 432** 4mm 3m m m m m 1  **215-220 43m** 4mm 3m m m m m 1  **221-230 m3m** 4mm 6mm 2mm 2mm 2mm 2mm 2

**162-167 3m1** 6mm 2mm 2 2 2mm 2 2

 **m2m** m 2mm m m m m 1  **2mm** 2mm m m m m m 1  **47-74 mmm** 2mm 2mm 2mm 2mm 2mm 2mm 2

**Group Point Group {001} {100} {110} {hk0} {h0l} {hhl} {hkl}** 

**mm2** m m 2mm m m m 1

**Group {001} {100} {110} {hk0} {h0l} {hhl} {hkl}** 

**321** 31m m 2 1 m 1 1

**31m** 6mm 2 2mm 2 2 2mm 2

**Group {100} {111} {110} {hk0} {hhl} {hhl} {hkl} h>l h<l** 

rotational symmetry) are chiral. The chiral orientations are highlighted in yellow.

**Point** 

X-ray diffraction (XRD) is a non-destructive technique that reveals crystallography of an unknown material using monochromatic X-rays. X-rays are generated by an X-ray tube that uses a high voltage to accelerate the electrons released by a cathode to a high velocity. The so generated electrons collide with a metal target, the anode, creating the Xrays. [36] Different X-ray sources are used based on the need. Tungsten or a crackresistant alloy of rhenium (5%) and tungsten (95%) are generally used in the medical field. When soft X-rays are needed for special applications like mammography, a molybdenum source is used. In crystallography, a copper target is most common, with cobalt often being used when fluorescence from iron content in the sample might otherwise present a problem. For a copper target, X-ray emissions commonly contains a continuous white radiation and two characteristic x-rays, Kα (λ = 0.15418 nm) and Kβ (λ = 0.13922 nm) leading from 2p 1s and 3p 1s transitions, respectively. In general, the Kα transition is more intense than Kβ, and is a combination of Kα1 and Kα2. This is because of the slight difference between two possible spin states of 2p electrons. Monochromatic Kα X-rays can be obtained by using suitable filters that absorb the unneeded white radiation and Kβ. For example, a Ni foil is commonly used for radiation of copper target. [37]

**Figure 1.** Stereographic projections of the A) (001) and B) (00-1) orientations of CuO. These two orientations are superimposable mirror images of each other; they are achiral. The radial grid lines on the stereographic projections correspond to 30o increments of the tilt angle, χ. C) the interface model of (00-1) CuO (front, blue Cu atoms) on (001) CuO (back, brown Cu atoms) with a common [010] directions. These two orientations are superimposed onto each other, indicating that they are achiral.

174 Recent Advances in Crystallography

**(C)** 

**(A) (B)** 

**Figure 1.** Stereographic projections of the A) (001) and B) (00-1) orientations of CuO. These two orientations are superimposable mirror images of each other; they are achiral. The radial grid lines on the stereographic projections correspond to 30o increments of the tilt angle, χ. C) the interface model of

(00-1) CuO (front, blue Cu atoms) on (001) CuO (back, brown Cu atoms) with a common [010] directions. These two orientations are superimposed onto each other, indicating that they are achiral.

**Figure 2.** Stereographic projections of A) (111) and B) (-1-1-1) orientation of CuO. These two orientations are nonsuperimposable mirror images of each other; they are chiral. The radial grid lines on the stereographic projections correspond to 30o increments of the tilt angle, χ. C) the interface model of (-1-1-1) CuO (red oxygen atoms) on (111) CuO (violet oxygen atoms) with a common [1-10] direction. These two surfaces are nonsuperimposable; therefore, they are chiral.

X-ray diffraction works on the principle of Bragg's law, nλ = 2d sin θ, where λ is the x-ray wavelength, d is the lattice spacing and θ is the Bragg angle. The layers of a crystal act like weak reflecting mirrors for the X-rays. Only if the path difference of the reflected X-rays is a whole number of wavelengths does constructive interference occurs, as shown in Figure 3.

In general, X-ray diffraction patterns are plots of intensity versus 2θ angle. Different planes in a crystal diffract at different angles giving a pattern which is unique to a crystal. The intensities of the reflections are determined by the distribution of the electrons in the unit cell. X-rays going through areas with high electron density will reflect strongly and areas with low electron density will give weak intensities. Therefore, every crystalline material has a unique X-ray diffraction pattern that can be used to determine the crystallinity and phase of the deposited material.

Thin films deposited on polycrystalline substrates can be analyzed by running two types of experiments. In the first case, a symmetric scan (gonio scan) can be used to evaluate the outof-plane texture of the film. It is a conventional θ-2θ scan for the Bragg-Brentano geometry. Figure 4 (A) shows a schematic representation of a gonio scan. Where, ω is the incident angle and θ is the diffracted angle.

**Figure 3.** Schematic representation of Bragg's law.

In a gonio scan, ω = θ and ω + θ = 2θ. Another way to characterize thin films is through glancing angle measurements, as shown in Figure 4 (B). In this case, ω + θ = 2θ and ω is fixed but θ varies. Glancing angle measurement is a good technique to measure polycrystalline grains. As the w is fixed and the θ is varied, all the planes in the material are brought into the Bragg condition. However, this technique cannot be used for highly oriented films or epitaxial films.

Epitaxial films deposited on single crystals are oriented both out-of-plane as well as inplane. In this case, X-ray characterization such as diffraction patterns, pole figures, azimuthal scans, and rocking curves are performed.

Unlike polycrystalline films, epitaxial films grow with one orientation and show only a family of planes in the pattern. In Figure 4, an epitaxial magnetite film deposited on a Ni(111) substrate shows only the {111} family peaks. [38] The experimental setup to determine out-of-plane orientation is similar to the gonio scan but instead a 2θ-omega scan is run. The difference between this and the gonio scan is that there can be an offset between 2θ and omega, so that omega = ½ 2θ + offset. This is useful when collecting a diffraction scan from an epitaxial film, when the tilt of the film is compensated by the offset. Identification of the pattern is done by comparing the pattern with the existing patterns in the database. For example, a magnetite film is identified by JCPDS#19-0629 pattern. However, this does not provide any information about in-plane orientation of the film. To determine the in-plane orientation of the film, X-ray pole figures and azimuthal scans are run. Pole figures can be used to probe planes which are not parallel with the geometric surface of the sample. The sample is moved through a series of tilt angles, χ, and at each tilt angle the sample is rotated through azimuthal angle, φ, of 0 to 360o. Peaks occur in the pole figure when the Bragg condition is satisfied. During the experiment 2θ is fixed, which is normally the highest intensity peak of a randomly oriented powder diffraction pattern of the material. Figure 6 is a schematic representation of a pole figure measurement. Azimuthal scans can be considered as a cross-section of a pole figure. They are obtained when the measurement is carried out at a specific 2θ for only specific tilt angle, χ, and rotated azimuthally, φ, from 0 to 360o. Comparing the azimuthal scans at specific tilt angle for a substrate and a film, we can obtain the epitaxial relationships.

176 Recent Advances in Crystallography

phase of the deposited material.

angle and θ is the diffracted angle.

**Figure 3.** Schematic representation of Bragg's law.

azimuthal scans, and rocking curves are performed.

oriented films or epitaxial films.

with low electron density will give weak intensities. Therefore, every crystalline material has a unique X-ray diffraction pattern that can be used to determine the crystallinity and

Thin films deposited on polycrystalline substrates can be analyzed by running two types of experiments. In the first case, a symmetric scan (gonio scan) can be used to evaluate the outof-plane texture of the film. It is a conventional θ-2θ scan for the Bragg-Brentano geometry. Figure 4 (A) shows a schematic representation of a gonio scan. Where, ω is the incident

In a gonio scan, ω = θ and ω + θ = 2θ. Another way to characterize thin films is through glancing angle measurements, as shown in Figure 4 (B). In this case, ω + θ = 2θ and ω is fixed but θ varies. Glancing angle measurement is a good technique to measure polycrystalline grains. As the w is fixed and the θ is varied, all the planes in the material are brought into the Bragg condition. However, this technique cannot be used for highly

Epitaxial films deposited on single crystals are oriented both out-of-plane as well as inplane. In this case, X-ray characterization such as diffraction patterns, pole figures,

Unlike polycrystalline films, epitaxial films grow with one orientation and show only a family of planes in the pattern. In Figure 4, an epitaxial magnetite film deposited on a Ni(111) substrate shows only the {111} family peaks. [38] The experimental setup to determine out-of-plane orientation is similar to the gonio scan but instead a 2θ-omega scan

**Figure 4.** Schematic representation of (A) gonio scan used for textured films and (B) glancing angle used for polycrystalline grains.

To determine the quality of epitaxy, X-ray rocking curves are run. The rocking curves indicate the mosaic spread of the film relative to the substrate. The larger the full width at half maximum (FWHM), the larger the mosaic spread. In the experimental setup for a rocking curve, only the omega axis is scanned as data are collected. All other axes, such as 2θ, are fixed at specific angles. In a perfect single crystal, the FWHM is small indicating that all domains are aligned. The width of the rocking curve is a direct measurement of the range of orientation of the sample. In general, the rocking curves are performed for substrate as

#### 178 Recent Advances in Crystallography

well as the film for comparison of mosaic spread. If the mosaic spread of the film is low and comparable to the substrate, the peaks in the pole figure become sharper and more intense. Rocking curves have been used to understand the in-plane misorientation of ZnO, AlN, and GaN on sapphire and MgO films grown on GaAs.

**Figure 5.** X-ray diffraction pattern of an epitaxial magnetite (Fe3O4) film on Ni(111) single crystal.
